Nonlinear robust estimation of linear parametric regression models-Based on empirical process theory

There is room for improvement in the efficiency of parametric estimation for the linear regression model and its robustness to heavy-tailed errors and outliers. This paper proposes an alternative robust regression method based on conditional distribution function of the dependent variable, and proves the consistency and asymptotic normality of the proposed estimator by using empirical process theory. Compared with ordinary least squares (OLS) estimator and two other usual least absolute deviations (LAD) and Huber robust estimators, the proposed estimator can grasp the whole distribution information of the dependent variable and more accurately uncover the true data generation process from the sample. It has better robustness to the heavy-tailed distribution of the error term. It is immune to the outlying observations and can be more easily weaken the bad effect of outliers on the parametric estimation. Simulation in various designs shows that the proposed estimator performs well in finite samples and is quite robust to the presence of heavy-tailed errors or outliers, and outperforms OLS, LAD and Huber estimators. © 2016, Editorial Board of Journal of Systems Engineering Society of China. All right reserved.